Quantum networks and quantum simulations with ions in an optical cavity

Ions in an optical cavity could serve as a light-matter interface within a quantum network, enabling distribution of quantum information over long distances. Toward this goal, we seek to build upon recent advances in the control of both laser-cooled, trapped ions and the coherent ion-cavity interaction. Using our recent demonstration of ion- cavity entanglement as a springboard, we now focus on the interaction of two atoms with a single cavity mode. We explore different methods of engineering entanglement between the atoms, and we investigate how increasing the atom number can improve the quality of an ion-photon interface. While other experiments have explored the collective interactions of large atom clouds with an optical cavity, these will be the first experiments in which the states of individual ions are measured and manipulated. A quantum computer that can outperform classical computers is still a long-term goal. However, it is anticipated that in the near future, quantum simulations may offer new insights into physical processes. In a quantum simulation, one quantum system reproduces the physics of another quantum system. Initial experiments have shown that trapped ion strings can emulate certain properties of discrete spin sytems, where the spins might represent, for example, electrons in a solid-state lattice. In a new proposal, we suggest that by coupling ions to an optical cavity, one can simulate continuous physical systems, that is, field theories. In this project, we develop an experimental realization in which an ion-cavity system simulates a well-known quantum field theory, the Lieb- Liniger Hamiltonian. Finally, the ability to observe interesting physical processes in atom-cavity systems is often limited by technology. In parallel with the experiments above, we pursue a new, fiber-based design for integrating an optical cavity with an ion trap. We anticipate that this design will bring us into a regime in which coherent processes dominate cavity dynamics.

Two mirrors facing one another form an optical cavity, in which light bounces back and forth from one mirror to the other, trapped between them. Placing single ions between the cavity mirrors allows us to study the interactions of the ions with light. We say that the cavity forms a quantum interface between individual ions and photons (quantum-mechanical particles of light). Such an interface could play an important role in future networks that link together quantum computers over long distances. The quantum interface would allow information to be transferred between ions and photons. Ions are leading candidates for storing and processing information in quantum computers, while the photons would carry information between remote computers, for example, over optical fibers. This project focused on the interaction of two ions with the cavity mode. We demonstrated a new method to entangle the ions with one another via the cavity. Entangled states are quantum-mechanical states in which the particles involved cannot be described separately from one another, and these states are an essential resource for quantum computing and quantum networks. In our experiment, we first entangled each of two ions with a photon. Then, by measuring the two photons, we entangled the ions with one another. In a second experiment with two ions, we showed that we could use entanglement between the ions as a resource to make information transfer between ions and photons more robust. We first transferred information encoded in a single ion onto a photon. Next, we encoded the same information within two entangled ios, and transferred that information onto a photon. We demonstrated that the second version of the process preserved the information more faithfully and made the transfer more efficient. We also showed that other entangled states could be used to decouple the ions from their interaction with photons in the cavity, that is, the interaction of the ions with light in the cavity could be tuned via the entanglement between the ions.Finally, the ability to observe interesting physical processes in ion-cavity systems is often limited by technology. In parallel with the experiments above, we have developed a new, optical-fiber-based design for integrating a cavity with an ion trap. Our design allows quantum-mechanical interactions to dominate the system dynamics by minimizing the interaction of the ions and photons with the environment, which disturbs the particles. We are currently testing the interactions of a single ion with this fiber cavity.